# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/arithmetic/LE__MULT__LCANCEL', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/arithmetic/LE__MULT__LCANCEL', aHLu_FALSITY)).
fof(3, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)|s(t_bool,X1)=s(t_bool,f)),file('i/f/arithmetic/LE__MULT__LCANCEL', aHLu_BOOLu_CASES)).
fof(5, axiom,![X7]:![X8]:![X9]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X8))))=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X7))),s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X7))))))),file('i/f/arithmetic/LE__MULT__LCANCEL', ah4s_arithmetics_LESSu_u_MONOu_u_MULT)).
fof(11, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)<=>p(s(t_bool,X1))),file('i/f/arithmetic/LE__MULT__LCANCEL', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(12, axiom,![X9]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/arithmetic/LE__MULT__LCANCEL', ah4s_arithmetics_MULTu_u_CLAUSESu_c1)).
fof(14, axiom,![X9]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X9)))),file('i/f/arithmetic/LE__MULT__LCANCEL', ah4s_arithmetics_LESSu_u_EQu_u_REFL)).
fof(18, axiom,![X8]:![X9]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X8)))=s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X9))),file('i/f/arithmetic/LE__MULT__LCANCEL', ah4s_arithmetics_MULTu_u_COMM)).
fof(25, axiom,![X8]:![X9]:(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X8)))=s(t_h4s_nums_num,h4s_nums_0)<=>(s(t_h4s_nums_num,X9)=s(t_h4s_nums_num,h4s_nums_0)|s(t_h4s_nums_num,X8)=s(t_h4s_nums_num,h4s_nums_0))),file('i/f/arithmetic/LE__MULT__LCANCEL', ah4s_arithmetics_MULTu_u_EQu_u_0)).
fof(54, axiom,![X7]:![X8]:![X9]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X8))),s(t_h4s_nums_num,X7)))=s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X7))),s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X7))))),file('i/f/arithmetic/LE__MULT__LCANCEL', ah4s_arithmetics_RIGHTu_u_SUBu_u_DISTRIB)).
fof(80, axiom,![X8]:![X9]:(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X8)))=s(t_h4s_nums_num,h4s_nums_0)<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X8))))),file('i/f/arithmetic/LE__MULT__LCANCEL', ah4s_arithmetics_SUBu_u_EQu_u_0)).
fof(133, conjecture,![X7]:![X8]:![X9]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X8))),s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X7))))))<=>(s(t_h4s_nums_num,X9)=s(t_h4s_nums_num,h4s_nums_0)|p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X7)))))),file('i/f/arithmetic/LE__MULT__LCANCEL', ch4s_arithmetics_LEu_u_MULTu_u_LCANCEL)).
# SZS output end CNFRefutation
